Well, I think Brazilian Portuguese is closer and closer to becoming a non-pro-drop language. But European Portuguese is not lagging that behind.
In Brazilian Portuguese, in my opinion, there's a tendency not to drop even the first person singular and plural (eu and nós) in the spoken language especially when they're first uttered:Eu* vi muita gente na rua e decidi** ir lá ver o que 'tava acontecendo.
* [it's for the first time uttered and although it could be dropped, it isn't]
** [Now the "eu" is dropped]

No, but only because of the first person. The second person conjugation, in Brazil, is not used anymore (both singular and plural), and the first plural person (nós) is getting replaced by another conjugation which is the same of the third singular.

Like Spanish, European Portuguese is almost exclusively pro-drop, but is it true that Brazilian Portuguese almost always uses pronouns?

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From my experience, I'd say the use of pronouns is indeed more frequent in Brazilian Portuguese. This is probably because Brazilians tend to use third-person forms for 'you', 'he/she/it' and 'we', thus having the necessity to specify their respective pronouns (você, ele/ela, a gente) - whereas in Portugal, the common use of second-person singular and first-person plural forms reduces the need of explicit pronouns.

Well, in my post I mainly talked about the first persons (eu and nós) because for the second and third persons it's quite obvious that pronoun is NOT dropped AT ALL.
And not to mention, of course, the ever-present "a gente" as the first person plural and it's never dropped.

Everyone can have a look at a video from someone in Brazil on YouTube speaking spontaneously or a conversation in a soap opera and try to identify how many times the pronouns are dropped. Very few.

Just like in RS, in my state PE the tu is used more than você among friends.
The "tu" is uttered, almost never dropped, but when it's dropped, the "s" comes back: Tu vai amanhã? OR Vais amanhã?

It must be interesting to be a stranger studying portuguese. You can take many different aspects from many variants and literally build your own language, and it'll still be right!

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Usually the Portuguese say that I speak Brazilian. When I speak with Brazilians I throw in some Portuguese slang. And they ask me the meaning.
In the new thread I opened, you see I've built my own system of possessive adjectives.

Like Spanish, European Portuguese is almost exclusively pro-drop, but is it true that Brazilian Portuguese almost always uses pronouns?

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In both brazilian and european Portuguese, it's unnecessary sometimes to let the subject (pronoun) explicit. If there is more than one person that matches with the verbal form, it's necessary to declare it. For example, the verb "estar" (to be). Eu estou, Tú estás, ele / você está, nós estamos, vós estáis, eles / vocês estão. Only Eu matches with estou, therefore, it's needless to declare it when you say "estou triste", the same happens to "estás, estamos, estáis". On the other hand, "está" matches with both ele and você, that's why if you ask someone "está triste?" without the subject, the person who you are talking to will ask you, "who? eu or ele / ela?". Depending on the context of the conversation, your interlocutor will understand that you are talking about him, but in the most of the cases, it begets ambiguity.
I think there should be in english this option as well. If only "I" am, and no other pronoun "he, she, we" matches with this word (am), why not to say "am happy"?

Hi.
I'm having a look at portuguese grammar and I got an idea of this matter.
Is it possible that you use personal subject pronouns "eu" and "nos" (even when there is a present, preterite or future indicative) because standard (formal) language rules don't allow you to start a sentence with a proclitic pronoun?

So, in EP one can say "digo-te/dizemos-te" or "amo-te" while in formal BP one have to say "eu te digo/nos te dizemos" or "eu te amo" instead of (the "wrong way") "te digo/te dizemos" or "te amo" (used only in very informal spoken language).

Could this syntactic rule be the reason why brazilian tend not to drop subject pronoun "eu" and "nos" even if verbal inflections are clear?

But I guess, it has to do with the rhythm too, many people use the introductory/first eu, and dismiss repeated usage afterwards, just like they dismiss initial article with possessive, and use ''linking'' article afterwards:

Many grammarians consider the overuse of explicit pronouns and explicit articles with possessives inelegant in formal texts tho'.
The more formal text is, the fewer articles and explicit pronouns you see. In newspapers headlines, the most formal style of all, you see the most extreme cases of dismissal of articles and pronouns.

Maybe the generalized use of pronouns started with reduction of verbal forms:

And since any language tends to symmetry (rather than assymetry),
it's easier to use always eu and nós in eu sei, nós iremos
than use it like this: eu queria, você queria, ele queria, queríamos, vocês queriam, eles queriam.

(I haven't counted, but I think in 90% cases Brazilians tend to say: eu sei, rather than bare sei,
except perhaps when answering a direct question: Cê sabe? -Sei.
But when commenting to something, I always heard them say: Eu sei,
this is similar to Spanish usage of Lo sé rather than Sé

Spoken Brazilian Portuguese deletes o, and makes up for this by using eu:

Asymmetry can cause dramatic changes in verbal paradigms.
In Latin, because future tense was formed differently in 1st and 2nd vs 3rd and 4th conjugation in Latin,
it was one of the first forms/tenses which got obsolete in spoken Latin, and none of the future Latin forms survived in Romance languages.
(Speaking of the Latin future: te amabo(= vou te amar) does look like um ama-bo (=eu te amo in CapeVerdian )

If we were to follow the advice given by some grammarians (dismiss the pronoun when it's not needed), we would create a fairly assimetric system:eu queria, você queria, ele queria, queríamos, vocês queriam, eles queriam (1)

Yes, that's it!
I think that when people are used to employing all subject pronouns in spoken language and when all professors everyday correct the absence of the pronouns "eu" and "nos" in sentences with clictic pronouns, one start to employ them almost ever.

Just like in RS, in my state PE the tu is used more than você among friends.
The "tu" is uttered, almost never dropped, but when it's dropped, the "s" comes back: Tu vai amanhã? OR Vais amanhã?

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There is something interesting about this. I have lived in Recife - PE and I noticed that there is very common the conjugation of the 2nd person, but with a little modification, they don't say de "t". So: Fizeste turns to Fizesse, Foste turns to Fosse, etc.

The imperative mood is an exception to this rule about using the explicit pronoun in the beggining of a sentence. Everyone in Brazil says very naturally: "Me dá uma chance", "Me faz um favor?". It's not unusual to hear someone say "Cê me faz um favor?", but perhaps in this case the speaker interprets the verb as indicative.